Just found the response on Quora about a similar question, how philosophical and mathematical logic differ. I have pasted one answer below as it tickled me.
“When I was getting my PhD, we had a joint logic seminar with both philosophical and mathematical logicians. I would say the most striking difference is what part of the talk they are interested in.
When a mathematical logician gives a talk in front of an audience that contains philosophical logicians, it often goes something like this. There is a brief introduction, including a couple of definitions. For the mathematical logician, this is just boring routine stuff, something you need to go through before you write down the theorem and gets to the interesting part, the neat techniques he or she invented to prove it.
However, as soon as the definitions are shown, the philosophers raise their hands and want to discuss whether this is the “right” definition. For them, the definition is supposed to clarify what you are studying; the definition itself should captures some underlying basic truth. The mathematical logician just doesn’t care about that. He or she will rather be thinking something along the lines of “Clearly it is the right definition, because that is the definition that lets us prove this extremely cool theorem that I haven’t even gotten to write down yet! Shut up and let me get on with it!””
What is the difference between philosophical logic & mathematical logic? - Quora
Philosophical and mathematical – but they are really the same thing. however there is a difference in how they are taught and used. From stack exchange… “The main difference between “Logic in Philosophy” and “Mathematical Logic” is that in the former case logic is used as a tool, while in the latter it is studied for its own sake.”
At my university, students majoring in philosophy take a course called “Logic in Philosophy” and there is also a course offered in the Math Department called “Mathematical Logic”. There are also
In logic, an argument can be invalid even if its conclusion is true, and an argument can be valid even if its conclusion is false. It’s a confusing concept, and people are easily fooled when …
Hmm, I thought this was a silly idea, but I just read on Wikipedia otherwise. That “In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics.”
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics. Higher-order logics with their standard semantics are more expressive, but their model-theoretic properties are less ... Read more
Just found the response on Quora about a similar question, how philosophical and mathematical logic differ. I have pasted one answer below as it tickled me.
“When I was getting my PhD, we had a joint logic seminar with both philosophical and mathematical logicians. I would say the most striking difference is what part of the talk they are interested in.
When a mathematical logician gives a talk in front of an audience that contains philosophical logicians, it often goes something like this. There is a brief introduction, including a couple of definitions. For the mathematical logician, this is just boring routine stuff, something you need to go through before you write down the theorem and gets to the interesting part, the neat techniques he or she invented to prove it.
However, as soon as the definitions are shown, the philosophers raise their hands and want to discuss whether this is the “right” definition. For them, the definition is supposed to clarify what you are studying; the definition itself should captures some underlying basic truth. The mathematical logician just doesn’t care about that. He or she will rather be thinking something along the lines of “Clearly it is the right definition, because that is the definition that lets us prove this extremely cool theorem that I haven’t even gotten to write down yet! Shut up and let me get on with it!””
Philosophical and mathematical – but they are really the same thing. however there is a difference in how they are taught and used. From stack exchange… “The main difference between “Logic in Philosophy” and “Mathematical Logic” is that in the former case logic is used as a tool, while in the latter it is studied for its own sake.”
I blame Spock. Mr, not Dr. Fake news at the most fundamental level.
Hmm, I thought this was a silly idea, but I just read on Wikipedia otherwise. That “In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics.”